Anomalous partially hyperbolic diffeomorphisms II: stably ergodic examples

TL;DR

This paper constructs specific examples of robustly transitive and stably ergodic partially hyperbolic diffeomorphisms on 3-manifolds, challenging existing classification conjectures by Pujals.

Contribution

It provides new counterexamples of partially hyperbolic diffeomorphisms with exponential fundamental groups that are not homotopic to the identity, expanding understanding of dynamical systems.

Findings

Examples of stably ergodic diffeomorphisms on 3-manifolds

Counterexamples to Pujals' classification conjecture

Diffeomorphisms with exponential fundamental groups

Abstract

We construct examples of robustly transitive and stably ergodic partially hyperbolic diffeomorphisms $f$ on compact $3$-manifolds with fundamental groups of exponential growth such that $f^n$ is not homotopic to identity for all $n>0$. These provide counterexamples to a classification conjecture of Pujals.